I have been finding that using the various tricks shared my community members and ultimaker staff here to dry out TPU — the low temp oven trick, similar to refreshing stereo audio tapes, or food dehydrator (like PrintDry or sorting out your own solution), or drying the filament on the bed overnight all lead to happier TPU processing. Any other trick that I am looking into that is new to me is bracing the Bowden tube up a few inches/cm so that the insertion angle is at a fixed true 90 degrees down into the hot end seems to reduce friction where it matters and allows retractions to perform more accurately even when being driven from a distant filament drive.
The results I have seen are a remarkable improvement, exciting in particular because this is even without changing anything other than drying the TPU and bracing the insertion point. But I have not attempted this new trick myself, just drying TPU which I certainly encourage, so I can only suggest that these are promising directions.
Depending on your type of use, you might consider crushing the TPU element a few 0.1s into the ABS. This is an old hack but I have liked it for living hinges and less compatible bonding.
Wanna share a photo or two of your attempts so far?

Hey Shaun!
There are a few answers there -- some high-tech solutions and some practical solutions. But it really comes down to the environment around your printer. If you are in, say, Arizona, you can basically ignore the worry and print away! If you are in Malaysia, you'd better come up with an end to end sealed filament box chock full of dessicant to help counteract the hygroscopic thirst of that material. There are a bunch of PVAs and some are thirstier than others. I have found the Ultimaker PVA a bit hardier than I'm used to from the early days of desktop 3D printing and PVA, but I defer to other's more recent experiences for formfutura etc.
I print multiple day prints with PVA all the time in Brooklyn, sometimes in my apartment that occasionally is blasted by steam heat (not too effective for heat, but hey), and sometimes at New Lab where humidity seems fairly consistent. And I haven't seen print-destroying degradation during long prints. I usually mess up my PVA when I complete a cool project and leave the PVA on the spool when I go on the road for a few weeks. d'oh! So remember when you aren't using it to box it up. And get it fully out of that BB core!
If humidity where you print is a tough issue, you might consider grabbing one of those food dehydrators like PrintDry kit Matterhackers offers. That gives you a shot to dry it out. It maybe just cargo cult, but this seems to restore waterlogged PVA spools better than the build-plate trick. But there are community members and staff here who swear by the overnight build plate trick.
There are some great PVA resources in this forums AMA event from this past summer:

Let me know if that technique is working for you! You can also take trusted elements and roll them into a machine and material profile etc. -- but I really like the Cura 3MF project files for templating right now. (Probably because I change slicing goals all the time, so am not zeroing in on only one.)

By the way, I don't recommend taking apart your core, @gr5 has hundreds of hours of experience under his belt with that, and there are parts that are easy to break if you dissemble. If the PVA has sorta glassed in there, trying to get it reamed out of there with hand tools will be frustrating and not that succesful. So your best bet is using the heater cartridge as still assembled to get things moving again. And keep @kmanstudios 's best practices in mind for backing out material from the core in mind for the future.
I'd suggest trying to cleaning examples above, grab cleaning sticks if you can (or us a high-temp warpy material like PC if you have some handy)
Where are you physically located? Just in case there are folks on the ground local to you who might have some tricks up their sleeves to help.

ah, heck. there was a bug, the bug was squashed, and then I used this tool happily just a few weeks ago in 3.1 with a whole workshop full of people. Can you share the resulting patch of gcode at that height to match with these settings? And of course the cura version.
I don't just want to help you (which I do of course), but I also need to use that plugin on Saturday!

there are a couple of places to check, but i have a quick (if not cheap) thing you should start with -- keep those settings and grab some better filament than that Hatchbox. I'm not saying hatchbox is bad, but i think you should look at two similar filaments from different vendors and see if you get similar results. And then drop the temperature 5degrees or so and try again.
How firmly is your bowden clamped on both ends? If there is play, well, that is not good. ;-)

that is not big. The check is opening it in meshlab, meshmixer, and checking the density of the triangles. If it is just black with tight triangles everywhere, you might not need that much resolution assigned to that geometry (so it might be introducing more lines of gcode to process than you need). If not, the problem is elsewhere.
Matt

Well, while there isn't a handy api resource page for you to help you understand and interpret the various settings, there ARE a number of great custom profiles and the Ultimaker machine profiles themselves that you can load and inspect to learn how they function. The "house style" for Ultimaker is to use a cascade to stack profiles against each other, so that tweaks for a particular model or configuration are later in the cascade of inheritance than the features that apply to more ranges of models and configurations earlier in the inheritance treee. What this also means for you is that you can setup a simple default profile for your custom machine, and then add other selectable configurations to tune or tweak to help with specific nozzle/hotend configurations. I wish we had a developers manual as well as an operating manual, but with Cura advancing so quickly, that's tough! Spend some time in some profiles and then see if you can ask some of your deeper questions here or at Freenode on IRC #cura or #cura-dev channels.

Note that gr5s suggestion works best after a successful print, etc., where one of the last end.gcode actions is to withdraw the filament a bit, enough that you can use the lever to pull away the tensioner and do exactly what he says! As a result, my machines when cold can work great for swapping material quickly even when I don't have time to load it officially. You miss out from recognizing the precise filament if you are using the Ultimaker filament, though.

I haven't seen an example where people have been dissolving away Breakaway Material, but it might help to note that there is a mix of PLA and TPU in this material. So the solvents like acetone and MEK would probably work BUT they would likely scar the PLA and needs some serious ventilation for you. It might work best to try a twisting action, should you be able to grip it, to dislodge it from the PLA so you can try to squeeze it out of tight openings. I'll keep my eyes out for tricks for trapped Breakway!

Grab meshmixer from Autodesk for free and you can use that to intelligently repair and decimate. You can also use Netfabb. But probably there are export resolution settings you can adjust for fewer polys and a similar printed result. Check the filesize of your STL and if it is really large, this is possibly having an effect.

yeah, I'd suggest taking a look at projects in the forums here, as well as checking out the how-tos for Octoprint out there in the world. There are some existing tools for octoprint that make this easier now, but there are also TONS of articles with details about which route to forward a port safely to access the camera. Combining those with some insights into how UM3 functions here from Daid will help:

@kmanstudios - what is your luck with the PrintDry for processing waterlogged full spools? That was its intention, though I haven't finished setting mine up to really use it. I hear it is fantastic for nylons.

The points in this thread about TPU (in each of its forms) being hygroscopic is worth taking seriously -- dry out that filament, and it will treat you better! but darned if I can fully eliminate retraction stringiness myself. I just tweak the model to prepare for this and disable retraction where I can. That won't necessarily help you now that you have something you want to print, but consider whether you can clip strings with a flush cutter afterwards....
I think you'd do fine with TPU 95A or NinjaTek's Cheetah -- very similar materials and the slightly less squishy durameter can make it easier to predict and print at higher speeds than NinjaFlex (at Shore 85A) and softer materials.

There are a bunch of places where you can grab a borosilicate glass place that will remain flat at high heat from many suppliers, not just for 3D printing. Though there are plenty of off-brand suppliers that will offer you cheap borosilicate glass printing plates at the same or better that you can get from a local glazier! I would not just use any sort of glass, especially if you play with materials like PC or tough nylons that might bond to glass and break it! You'll cut yourself!
But that said, glad you are able to make progress and get some good prints off of there, though. Those projects are starting to look great!
One quick note re: hairspray. The reason people use cheap hairsprays like Acquanet is because ... it has a lot of PVA glue in it. Yep, this is glue for your hair -- which might explain why it is so aggressively effective at sticking things in place, and then washes away in the shower. Well, spray dispensing it is kinda handy (you need so little) until you start gumming up your drive rods over time. But what about a glue stick? Or grab a polyester sticker label or a piece of PEI material, and you'll be happier. Or BuildTak and its peers! I am no fan of hairspray these days, but the good news is that which "flavor" of PVA you use will probably work fine, as long as you don't pick one (like UHU gluesticks over time!) that crusts over between heating cycles, requiring you to clean the plate and re-apply.
As for z-hop and cura ... well, it works in certain cases, but might not be doing what you assume for a z-hop. If you look at the paths in the layer viewer you may see some oddities in the paths that explain what happens with your actual print. If you just want clean top surfaces, look at the "ironing" features to do another pass with the nozzle at the end to rework the top surface and help eliminate some travel scars and other weirdness.
Matt